For a few years, by the time December rolls around, I am so beat up by daily grading, making copies, paperwork, being a good example for the youth of America, etc etc, that my Surface Area/Volume unit has always been just fantastically awful. Although it's been a long December, I was determined to make this at least a little better.

I start with surface areas, because we just spent tons of time working with areas of composite figures and shaded regions, so it makes sense to extend that.

So to start out, instead of this (try not to barf:)

I sneakily ask them to calculate some composite areas.

I am not super-thrilled with these. In the future I would make them bigger and use more integral values, and not use such a tall, skinny cone.

As they were working, I asked them to write how they calculated the area in the middle of the shape. So in that last one they might write "Area = 1 rectangle and 2 circles."

The cylinder was VERY interesting, since there's really nothing given about the height of the rectangle, but by now they tend to assume that if they need a dimension, there should be a way to figure it out. Some kids realized we were going to turn it into a cylinder and used the circumference of the circles, but some kids estimated that the height of the rectangle was about three circles, which I didn't anticipate but hey, pi is about 3, and that's kind of awesome.

Anyway, so now we are going to cut these out and hold on to them for a few days.

Hopefully avoiding the phenomenon of having no idea which dimensions we need or randomly plugging given numbers into given formulas.

I don't really know where we're going to go from here. I might freak out and go back to a traditional approach, but at least more kids might have a better idea of what those formulas are all about.